A first order reaction takes 40 min for 30% decompositon.

Explanation

(i) To find k value `[R]_(0) = 100 [R] = 100 - 30 = 70, t = 40` min
`k = (2.303)/(t) log ""([R]_(0))/([R]), k = (2.303)/(40) log ""(100)/(70)`
`k = (2.303)/(40) xx 0.1549, k = 8.92 xx 10^(-3)` min.
(ii) To find `t_(1//2)`
`t_(1//2) = (0.693)/(k) = (0.693)/(8.92xx10^(-3)) = 77.7` min.